The background service starts on its own every time you log in.
If this Mac still needs something set up (your vault, or a permission in System Settings), a Terminal window called Set Up This Mac opens once to walk you through it. It only answers Enter, s or q — type anything else in your own Terminal window. You can open it again any time with baton init --permissions.
To check on it, open Terminal and type baton status.
If something did not go to plan, the details are in ~/Library/Logs/baton-install.log.